# Accelerating the discovery of steady-states of planetary interior dynamics with machine learning

arXiv: https://arxiv.org/abs/2408.17298 · HTML: https://mlsanity.com/paper/2408.17298/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 64 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [Unfolding Time: Generative Modeling for Turbulent Flows in 4D](https://mlsanity.com/paper/2406.11390/) (2024)
- [Deep learning for surrogate modelling of 2D mantle convection](https://mlsanity.com/paper/2108.10105/) (2021)
- [ExoMDN: Rapid characterization of exoplanet interior structures with Mixture Density Networks](https://mlsanity.com/paper/2306.09002/) (2023)
- [Residual Neural Networks for the Prediction of Planetary Collision Outcomes](https://mlsanity.com/paper/2210.04248/) (2022)
- [NeuralCMS: A deep learning approach to study Jupiter's interior](https://mlsanity.com/paper/2405.09244/) (2024)

## Built on by (most cited first, 3 of 3)

- [Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations](https://mlsanity.com/paper/2505.14704/) (2025)
- [HydroStartML: A combined machine learning and physics-based approach to reduce hydrological model spin-up time](https://mlsanity.com/paper/2504.17420/) (2025)
- [Physics-based machine learning for mantle convection simulations](https://mlsanity.com/paper/2505.16041/) (2025)

## Abstract (arXiv)

Simulating mantle convection often requires reaching a computationally expensive steady-state, crucial for deriving scaling laws for thermal and dynamical flow properties and benchmarking numerical solutions. The strong temperature dependence of the rheology of mantle rocks causes viscosity variations of several orders of magnitude, leading to a slow-evolving stagnant lid where heat conduction dominates, overlying a rapidly-evolving and strongly convecting region. Time-stepping methods, while effective for fluids with constant viscosity, are hindered by the Courant criterion, which restricts the time step based on the system's maximum velocity and grid size. Consequently, achieving steady-state requires a large number of time steps due to the disparate time scales governing the stagnant and convecting regions. We present a concept for accelerating mantle convection simulations using machine learning. We generate a dataset of 128 two-dimensional simulations with mixed basal and internal heating, and pressure- and temperature-dependent viscosity. We train a feedforward neural network on 97 simulations to predict steady-state temperature profiles. These can then be used to initialize numerical time stepping methods for different simulation parameters. Compared to typical initializations, the number of time steps required to reach steady-state is reduced by a median factor of 3.75. The benefit of this method lies in requiring very few simulations to train on, providing a solution with no prediction error as we initialize a numerical method, and posing minimal computational overhead at inference time. We demonstrate the effectiveness of our approach and discuss the potential implications for accelerated simulations for advancing mantle convection research.